A continuous grinding machine of the above-mentioned kind is for example known from EP 155 380 B1. In practise it has become apparent that in many cases the desired grinding result cannot be achieved during one single passage of the workpiece through the grinding station. In case a further machining step is needed, the workpieces either have to be transported back to the machine infeed, which involves additional work expense and time loss, or the machine has to be provided with one or more additional grinding stations which are subsequently passed through by the workpieces, whereby the mechanical efforts, required space, and power consumption are increased during operation.